Simplify (a^2+7a+10)/(a^2+2a-15)+10/(a-3)

$\frac{a^{2} + 7 a + 10}{a^{2} + 2 a - 15} + \frac{10}{a - 3}$

Step 1

Simplify each term.

Factor $a^{2} + 7 a + 10$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $10$ and whose sum is $7$ .

$2, 5$

Write the factored form using these integers.

$\frac{(a + 2) (a + 5)}{a^{2} + 2 a - 15} + \frac{10}{a - 3}$

Factor $a^{2} + 2 a - 15$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 15$ and whose sum is $2$ .

$- 3, 5$

Write the factored form using these integers.

$\frac{(a + 2) (a + 5)}{(a - 3) (a + 5)} + \frac{10}{a - 3}$

Cancel the common factor of $a + 5$ .

Cancel the common factor.

$\frac{(a + 2) (a + 5)}{(a - 3) (a + 5)} + \frac{10}{a - 3}$

Rewrite the expression.

$\frac{a + 2}{a - 3} + \frac{10}{a - 3}$

Step 2

Combine fractions.

Combine the numerators over the common denominator.

$\frac{a + 2 + 10}{a - 3}$

Add $2$ and $10$ .

$\frac{a + 12}{a - 3}$

Simplify (a^2+7a+10)/(a^2+2a-15)+10/(a-3)

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